Question

A previous Arizona state lottery called Lotto is played as follows: The player selects six numbers from the numbers 1-42 and buys a ticket for $1. There are six winning numbers, which are selected at random from the numbers 1-42. To win a prize, a Lotto ticket must contain three or more of the winning numbers. A probability distribution for the number of winning numbers for a single ticket is shown in the following table.

a. If you buy one Lotto ticket, determine the probability that you win a prize. Round your answer to three decimal places.
b. If you buy one Lotto ticket per week for a year, determine the probability that you win a prize at least once in the 52 tries.